Solve for $x$ and $y$ using elimination. $\begin{align*}3x-5y &= -5 \\ -8x+6y &= 2\end{align*}$
We can eliminate $y$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $6$ and the bottom equation by $5$ $\begin{align*}18x-30y &= -30\\ -40x+30y &= 10\end{align*}$ Add the top and bottom equations. $-22x = -20$ Divide both sides by $-22$ and reduce as necessary. $x = \dfrac{10}{11}$ Substitute $\dfrac{10}{11}$ for $x$ in the top equation. $3( \dfrac{10}{11})-5y = -5$ $\dfrac{30}{11}-5y = -5$ $-5y = -\dfrac{85}{11}$ $y = \dfrac{17}{11}$ The solution is $\enspace x = \dfrac{10}{11}, \enspace y = \dfrac{17}{11}$.